Solving Systems of Fixpoint Equations via Strategy Iteration

Fixpoint equations and systems of equations are ubiquitous in model checking, so a recurring problem is how to solve them. Often however it's enough to know whether a member of the domain is under a certain element of the solution. This is known to be equivalent to a parity game, which can be solved by various algorithms. We'll focus on adapting a local strategy iteration algorithm for parity games to solve this reduced problem for fixpoint systems and comparing it with alternative solutions.